Frequency-selective surfaces (FSSs) have attracted great attention owing to their unique feature to manipulate transmission performance over the frequency domain. In this work, a filtering antenna-filtering antenna (FA-FA) FSS with a wide passband and double-side sharp roll-off characteristics is presented by inter-using the filtering antenna and receiving–transmitting metasurface methods. First, a dual-polarized filtering antenna element was designed by employing a parasitic band-stop structure with an L-probe feed. Then, the FA-FA-based FSS unit was constructed by placing two such filtering antennas back to back, with their feedings connected through metallic vias. Finally, the FSS with a wide passband and high selectivity was realized by arraying the FA-FA units periodically. The full-wave simulation results demonstrated that the designed FA-FA-based FSS had a wide passband from 13.06 GHz to 14.46 GHz with a flat in-band frequency response. The lower and upper roll-off bandwidths were sharp, reaching 1% and 1.2% of the center frequency. The proposed FA-FA-based FSS was fabricated and measured, achieving the coincident performance according to the theoretical prediction. The wideband band-pass FSS obtained a sharp double-side roll-off feature, which can be applied in various studies such as an antenna array, metasurface, communication, etc.